通过Thue--Morse词分离$γ$和$b$
A Separation of $γ$ and $b$ via Thue--Morse Words
摘要：
证明了对于$n\geq 2$，$n$第四个Morse字$t_n$的最小双向方案的长度$b(t_n)$是$n+2$ .由于Kutsukake等人[SPIRE 2020]表明$t_n$的最小弦吸引子的大小$γ(t_n)$是$n \geq 4$的$4$，这首次表明最小弦吸引子$γ$的大小和最小双向方案$b$的大小之间存在分离，即，存在这样的字符串族：$γ= o(b)$。
英文摘要：
We prove that for $n\geq 2$, the size $b(t_n)$ of the smallest bidirectional scheme for the $n$th Thue--Morse word $t_n$ is $n+2$. Since Kutsukake et al. [SPIRE 2020] show that the size $γ(t_n)$ of the smallest string attractor for $t_n$ is $4$ for $n \geq 4$, this shows for the first time that there is a separation between the size of the smallest string attractor $γ$ and the size of the smallest bidirectional scheme $b$, i.e., there exist string families such that $γ= o(b)$.
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